已知a>0,b>0,c>0且a+b+c=1,求 证1⼀a+1⼀b+1⼀c>=9?

2025-01-21 09:22:31
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回答1:

解,1/a+1/b+1/c =(a+b+c)/a+(a+b+c)/b+1(a+b+c)/c =1+b/a+c/a+1+a/b+c/b+1+a/c+b/c ≥3+2√(b/axa/b)+2√(c/axa/c)+2√c/bxb/c =9芸共.其中a=b=c=1/3 分析1=a+b+c,由想做尖子生去了解 全权方和不等式